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Nonclassical Symmetries for Nonlinear Diffusion and Absorption
Author(s) -
Arrigo D. J.,
Hill J. M.
Publication year - 1995
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm199594121
Subject(s) - homogeneous space , symmetry (geometry) , thermal diffusivity , nonlinear system , diffusion , exponential function , diffusion equation , class (philosophy) , physics , mathematical analysis , mathematics , statistical physics , quantum mechanics , geometry , computer science , economy , artificial intelligence , economics , service (business)
Nonclassical symmetry methods are used to study the nonlinear diffusion equation with a nonlinear source. In particular, exponential and power law diffusivities are examined and we obtain mathematical forms of the source term which permit nonclassical symmetry reductions. In addition to the known source terms obtained by classical symmetry methods, we find new source terms which admit symmetry reductions. We also deduce a class of nonclassical symmetries which are valid for arbitrary diffusivity and deduce corresponding new solution types. This is an important result since previously only traveling wave solutions were known to exist for arbitrary diffusivity. A number of examples are considered and new exact solutions are constructed.